Only two late tries from Isaia Toeava and John Afoa took the game away from Wales who had been within a single score of the world's best team for large parts of a hugely entertaining encounter in Cardiff.
Wales trailed 13-12 after 50 minutes and 23-18 with 71 minutes gone before the All Blacks pulled away to finish their European tour on a huge high.
And although Gatland admitted his men were bitterly disappointed not to secure an historic win, he insisted that playing the top sides in the world is by far the best way to improve ahead of next year's World Cup.
"We'd love to play them next week and the week after that and the week after that because that's how you improve and that's how you get better," said Gatland after the All Blacks completed a third Grand Slam tour in five years.
"That's how players learn and improve in this arena - by testing themselves against the best at the highest intensity. We've got to keep learning from that and keep being hard on ourselves.
"There's been certain aspects of our game that have improved, particularly how well we're able to compete with these sides up front, but there's some areas that are concerning. There's been some critical moments and turnovers and a little bit of
inaccuracy that have been costly.
"We felt at 13-12 that we had some momentum. Defensively we looked strong. The guys had confidence ad New Zealand looked a little bit rattled. To miss touch and for them to score from that was a critical.
"Those are the sort of things I am talking about that we have to eradicate from our game and learn from. Those are key moments that can be costly. We've improved massively as a side since 2008 but we need to stop shooting ourselves in the foot.
"Matthew Rees said the players had to be prepared to point fingers at each other and be hard on ourselves if we want to continue to improve as a side.
"A couple of years ago a lot of those players would have been patting each other on the back by pushing the All Blacks so close. But the boys are disappointed and know they are not far away from getting that crucial win against one of these big sides."